Ardashir Mohammadzadeh; Mohammad Hosein Sabzalian; Chunwei Zhang; Oscar Castillo; Rathinasamy Sakthivel; Fayez F. El-Sousy Springer International Publishing AG (2022) Kovakantinen kirja
Ardashir Mohammadazadeh; Mohammad Hosein Sabzalian; Oscar Castillo; Rathinasamy Sakthivel; Fayez F. M. El-Sousy; S Mobayen Springer (2022) Kovakantinen kirja
Ardashir Mohammadzadeh; Mohammad Hosein Sabzalian; Chunwei Zhang; Oscar Castillo; Rathinasamy Sakthivel; Fayez F. El-Sousy Springer (2023) Pehmeäkantinen kirja
Ardashir Mohammadazadeh; Mohammad Hosein Sabzalian; Oscar Castillo; Rathinasamy Sakthivel; Fayez F. M. El-Sousy; S Mobayen Springer (2023) Pehmeäkantinen kirja
This monograph establishes a theory of classification and translation closedness of time scales, a topic that was first studied by S. Hilger in 1988 to unify continuous and discrete analysis. The authors develop a theory of translation function on time scales that contains (piecewise) almost periodic functions, (piecewise) almost automorphic functions and their related generalization functions (e.g., pseudo almost periodic functions, weighted pseudo almost automorphic functions, and more). Against the background of dynamic equations, these function theories on time scales are applied to study the dynamical behavior of solutions for various types of dynamic equations on hybrid domains, including evolution equations, discontinuous equations and impulsive integro-differential equations. The theory presented allows many useful applications, such as in the Nicholson`s blowfiles model; the Lasota-Wazewska model; the Keynesian-Cross model; in those realistic dynamical models with a more complex hibrid domain, considered under different types of translation closedness of time scales; and in dynamic equations on mathematical models which cover neural networks. This book provides readers with the theoretical background necessary for accurate mathematical modeling in physics, chemical technology, population dynamics, biotechnology and economics, neural networks, and social sciences.